Physics
Wien's Displacement Law
Quick fact
The surface of the Sun (about 5,500°C) peaks in the yellow-green part of the spectrum, which is why we see it as white in space. Cooler red stars peak in the infrared, while hotter blue stars peak in the ultraviolet.
Why this is interesting
Why does a piece of metal glow red when hot, then white, then blue as it heats up? The answer lies in a simple but powerful rule: as temperature rises, the peak color of emitted light shifts to shorter wavelengths.
Read the full explanation
Understanding Wien's Displacement Law
Imagine a perfect blackbody—an object that absorbs all light and emits thermal radiation based solely on its temperature. Its emission curve has a distinct peak: the wavelength where it radiates most intensely. Wien's displacement law says that this peak wavelength (λmax) multiplied by the temperature (T) is constant: λmax × T = b, where b is Wien's constant (about 2.9 mm·K). For instance, a room-temperature object (300 K) peaks at about 9.7 micrometers (infrared), while a hot star at 30,000 K peaks at about 0.1 micrometers (ultraviolet). As temperature doubles, the peak shifts to half the wavelength.
A deeper explanation
Wien's displacement law arises from the thermodynamics of blackbody radiation. It was derived by Wilhelm Wien in 1893 using thermodynamic arguments before the full quantum theory of Planck. The law emerges from the fact that the spectral radiance per unit wavelength has a maximum whose position scales inversely with temperature. This relationship is a direct consequence of the shape of Planck's law, which describes the full spectrum. Intuitively, higher temperature means more energetic photons, so the average photon wavelength decreases. The law is crucial for determining the temperature of distant stars (by their color), for designing infrared detectors, and for understanding the cosmic microwave background (peak at 1.06 mm corresponds to 2.7 K). It connects everyday phenomena—like the color of a glowing ember—to the fundamental physics of thermal radiation.